Saturday, February 13, 2016

Crossover Basics

Introduction

This is a very simple introduction for non-engineering students who want to learn about the electronic parts that make up a speaker system. Math is not forgotten, it is deliberately excluded from this posting to give the budding speaker designer an easy introduction into the range of topics that go into speaker crossover networks and their design. It's by no means intended to be a canonical reference, but rather a tasty first meal. My hope is that readers whose interest remain piqued after reading this will be much more willing to learn the math that underpins crossover design as opposed to being overwhelmed by it.

Drivers

A speaker driver is the moving motor in a speaker. It is what takes electrical power on two inputs and on the other side produces sound. Most high quality modern speakers have drivers of different sizes. That's
because no one driver can handle every note. Much like an orchestra, or
a band. The lower the note, the bigger the driver. The higher the
note, the smaller. At the very least a speaker will have a tweeter for
the high notes and a woofer for the bass.

There are of course single-driver (i.e. Full-Range) speakers used by cheap electronics manufacturers as well as boutique makers which do not use crossovers at all. They are out of scope for this post.

Crossover Parts

The two most common parts in a crossover are
capacitors and inductors. Think of them like bouncers. More rare, and much simpler are resistors. In general they
behave like this:

The last part that is commonly used is a resistor. Resistors
resist the flow of current, hopefully evenly at all frequencies. Another
way to think of them is that they take voltage away from other
components by using it for themselves.

Also keep in mind that the term "block" here is not an absolute firewall. When we say capacitors block low frequencies, the amount they block varies by frequency. This is why Farads matter. The same for coils. The mH give us an indication of just how much they will block at each frequency we care about. A better word than block might be "slow" or "limit."

Simple Crossover

Now that we've discussed the parts you'll need to be familiar with, let's take a look at a schematic. We'll use XSim to create our images and charts. It's a free tool created by Bill Waslo, a regular at the DIY forums and the author of OmniMic. I encourage you to get your free copy of XSim here and follow along with the examples.

Schematics
are engineering maps to how electricity should flow in a circuit. The
image above shows a schematic using the simplest possible
crossovers on a tweeter (S1) and woofer (S2). The capacitor is shown as C1, the inductor is L1. The
triangle is the ground. The ground symbol is a type of short hand to
show that they are all connected together. Crossovers can get far more
complicated than this, but for mods it won't matter to you.
(queue evil laughter)

The
confusing part for beginners is that a schematic does not show the
physical relationship of the parts, or their physical size either. All
we can see here is the electrical values. After reading this blog
you'll want to examine a physical crossover and see if you can
identify the pathways to each driver yourself.

The parts here, C1 and L1, are connected in series with the drivers. That is, electricity must flow from one to the other. We can use XSim's Frequency Response Plot to show how the parts are working together.

The black line is the electro-acoustical sum of the effects of the speaker drivers plus the crossovers.You can see the tweeter's new response in red. Now the tweeter response, instead of being ideal (impossible in the real world), slopes upwards until 1kHz at a rate of 6dB/octave. For the woofer, in yellow, the coil causes a complementary effect. The woofer response now slopes downwards at a rate of 6dB/octave after 1kHz.

We call the 1 kHz bend the "knee" of the curve. this is where the rate changes from it's normal slope (6/12/18 dB per octave) to asymptotically approaching flat. At it's flattest is where our filters have ceased to do anything useful.

Second Order High Pass Filter

Let's
take a look at a more complicated schematic, where we will add parallel
components. In this example we've added L2, which is said to be
parallel to the tweeter.

You should also be aware that you may have multiple parts in series.
That is, you may have C1, L2, and then C2 in the tweeter section. That's
pretty common. Woofer and midrange drivers may also have multiple
parts. We'll cover this more below under "What's the Difference?"

The
last thing to do is show a resistor. Often designers have to work with
parts that don't match up completely in terms of voltage sensitivity.
That is, one driver will naturally be louder than another. They fix this
with resistors, and commonly use an L-pad to maintain the correct
driver impedance while changing the volume of the driver. Here is just
such an example.

R1
and R2 make up the L-pad we were discussing, so named because of the
shape it takes in the schematic. Since R2 is parallel with the driver
it reduces the apparent resistance of the tweeter, which may save
money. That's a more advanced topic. The crossover designer may use
just a series resistor as an alternative design, and it's a perfectly
valid approach depending on the other components of the circuit.

What's the Difference?

We are adding "poles" to the design. That
is, we are adding parts which add 6dB/octave of slope with each part.
Consider this example, with three identical ideal drivers. Each driver has a
different 1kHz high-pass filter between it and the amplifier. Of course, no one should actually build a speaker with 3 drivers like this! It's just for illustration:

As you have hopefully guessed, S1 uses a first order, S2 a second order and S3 a third order high-pass filter. You can see how the slope of the crossover changes as the poles are added below:

As the order (number of poles) of the filter gets higher, the slope gets steeper. The normal slope for first, second and third order filters is 6 dB, 12 dB and 18 dB per octave, or 6 dB x filter order. I say "normal" because after the first order, you can play somewhat with the bump and final filter slope. If you notice here, the second and third order filters start to develop a bit of a bump before rolling downwards. This is out of scope of our discussions here, just know that the filter order are general terms, not absolutes.

Low Pass Filter Examples

Now that you are familiar with the idea of filter order and poles, let's show you the same idea only using low pass filters instead, again with a knee on 1 kHz and ideal 8 Ohm drivers.

Notice that the order of the coils and caps is now reversed, but the number of the parts is consistent. As you can see, coils and caps while not mirror images of each other, are complementary. That coils and capacitors exist is proof enough to me that if there is any divine influence on the physics of this world then that divine presence intends for us to listen to good music for all of our lives. The slopes and phase angle changes for low pass filters are what we described before. 6dB, 12dB and 18 dB for first, second and third order filters, respectively but sloping in a different direction.

Before You Leave

It's important to note that throughout this post we've been using "ideal" drivers with exactly 8 Ohms of resistance and a flat, infinitely wide frequency response. In the real world speakers are not flat. Every real world loud speaker driver ever made is actually a type of band-pass device, with upper and lower limits. The effects of the crossover slopes are additive to the frequency response of the driver, not independent of them. We'll cover that topic more in the future.

Congratulations! You now know some basic ideas about speaker crossovers: